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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
755a4af4f86ea82b1ccc7709eab4bfc7aa1005b1 | f2fbd9ce3f46053c664b74a5294d7d2f584e72d3 | /src/for_mathlib/data/set/basic.lean | 2c61c16c94f1e5971a3aea5bdd5e6f0b05254834 | [
"Apache-2.0"
] | permissive | jcommelin/lean-perfectoid-spaces | c656ae26a2338ee7a0072dab63baf577f079ca12 | d5ed816bcc116fd4cde5ce9aaf03905d00ee391c | refs/heads/master | 1,584,610,432,107 | 1,538,491,594,000 | 1,538,491,594,000 | 136,299,168 | 0 | 0 | null | 1,528,274,452,000 | 1,528,274,452,000 | null | UTF-8 | Lean | false | false | 708 | lean | import data.set.basic
variables {Ξ± : Type*} {Ξ² : Type*}
namespace set
lemma prod_quotient_preimage_eq_image [s : setoid Ξ±] (g : quotient s β Ξ²) {h : Ξ± β Ξ²} (Hh : h = g β quotient.mk) (r : set (Ξ² Γ Ξ²)) :
{x : quotient s Γ quotient s | (g x.1, g x.2) β r} =
(Ξ» a : Ξ± Γ Ξ±, (β¦a.1β§, β¦a.2β§)) '' ((Ξ» a : Ξ± Γ Ξ±, (h a.1, h... |
0c39e81535c88da7ee6301de2551e473b6bfdb5a | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/playground/map_perf.lean | d2626333c68549ad0fd0e4ecf2dd036ebedf6001 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 843 | lean | abbrev Map1 : Type := RBMap Nat Bool (Ξ» a b, a < b)
abbrev Map2 : Type := HashMap Nat Bool
def mkMap1Aux : Nat β Map1 β Map1
| 0 m := m
| (n+1) m := mkMap1Aux n (m.insert n (n % 10 = 0))
def mkMap2Aux : Nat β Map2 β Map2
| 0 m := m
| (n+1) m := mkMap2Aux n (m.insert n (n % 10 = 0))
def mkMap1 (n : Nat) :=
mkMap1Aux ... |
e68cb3d0ee6a95d66dddafdff9b24e8a70d8b333 | 492a7e27d49633a89f7ce6e1e28f676b062fcbc9 | /src/monoidal_categories_reboot/unitors_equal.lean | a7b0811813a8d71ed201304d0d10579aaed98cbe | [
"Apache-2.0"
] | permissive | semorrison/monoidal-categories-reboot | 9edba30277de48a234b63813cf85b171772ce36f | 48b5f1d535daba4e591672042a298ac36be2e6dd | refs/heads/master | 1,642,472,396,149 | 1,560,587,477,000 | 1,560,587,477,000 | 156,465,626 | 0 | 1 | null | 1,541,549,278,000 | 1,541,549,278,000 | null | UTF-8 | Lean | false | false | 4,965 | lean | import .monoidal_functor_attributes
import tactic.slice
universes v u
namespace category_theory
open category_theory.category
open category_theory.monoidal_category
variables {C : Sort u} [π : monoidal_category.{v} C]
include π
namespace unitors_equal
lemma cells_1_2 : (Ο_ (π_ C)).hom = (Ξ»_ ((π_ C) β (π_ C)))... |
16398c033e4bcd3dd548014f568bd4554e1d962c | 874a8d2247ab9a4516052498f80da2e32d0e3a48 | /Fermat_little_v2.lean | ec70e095132e0e1bcdde57da4a5bb6c3888d33ad | [] | no_license | AlexKontorovich/Spring2020Math492 | 378b36c643ee029f5ab91c1677889baa591f5e85 | 659108c5d864ff5c75b9b3b13b847aa5cff4348a | refs/heads/master | 1,610,780,595,457 | 1,588,174,859,000 | 1,588,174,859,000 | 243,017,788 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 4,449 | lean | import data.nat.gcd
import algebra.big_operators
import data.zmod.basic
def divides (d n: β€):= βl:β€, n = d*l
def is_congruent_mod_n (a b n: β€) := divides n (b-a)
def relatively_prime(a b:β€) := βl:β€, Β¬(divides l a) β¨ Β¬(divides l b)
theorem relatively_prime_sum_to_one (a b : β€) (h : relatively_prime a b) :
β m n: ... |
4cc13a2a18183168e6af0c56760f0435d002efd2 | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/ring_theory/polynomial/dickson.lean | e03e41fd50196a0d1f0fd24cc25b6c9d7d99da96 | [
"Apache-2.0"
] | permissive | hikari0108/mathlib | b7ea2b7350497ab1a0b87a09d093ecc025a50dfa | a9e7d333b0cfd45f13a20f7b96b7d52e19fa2901 | refs/heads/master | 1,690,483,608,260 | 1,631,541,580,000 | 1,631,541,580,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,509 | lean | /-
Copyright (c) 2021 Julian Kuelshammer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Kuelshammer
-/
import ring_theory.polynomial.chebyshev
import ring_theory.localization
import data.zmod.basic
import algebra.char_p.invertible
/-!
# Dickson polynomials
... |
235c0672f4979152f0d37005e6e37c0b862f8388 | a0e23cfdd129a671bf3154ee1a8a3a72bf4c7940 | /stage0/src/Lean/Meta/Match/Basic.lean | f8917e589a94df3be1ca9b157fabcfb9e4f4a4a7 | [
"Apache-2.0"
] | permissive | WojciechKarpiel/lean4 | 7f89706b8e3c1f942b83a2c91a3a00b05da0e65b | f6e1314fa08293dea66a329e05b6c196a0189163 | refs/heads/master | 1,686,633,402,214 | 1,625,821,189,000 | 1,625,821,258,000 | 384,640,886 | 0 | 0 | Apache-2.0 | 1,625,903,617,000 | 1,625,903,026,000 | null | UTF-8 | Lean | false | false | 12,634 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Meta.Check
import Lean.Meta.Match.MatcherInfo
import Lean.Meta.Match.CaseArraySizes
namespace Lean.Meta.Match
/--
Auxiliary annotation used ... |
4fb82d3f72eb860f91169639cc3a8e98207c7426 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /test/equiv.lean | 07da7917028c40a3fd7f992da0d2edb44f8bbea5 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 400 | lean | import data.set.finite
import data.finset.image
def s : finset (fin 3) := {0, 1}
example : finset (fin 3) := s.map (equiv.add_left (1 : fin 3)).to_embedding
example : finset (fin 3) := s.map (equiv.add_left (1 : fin 3))
def f : equiv (fin 3) (fin 3) :=
{ to_fun := Ξ» x, x + 1,
inv_fun := Ξ» x, x - 1,
left_inv := d... |
68975ca22aea4e2177c2088a566eb1588fa4cb62 | 07c76fbd96ea1786cc6392fa834be62643cea420 | /hott/algebra/trunc_group.hlean | 9ad307ff4fdd24a23ea8da70dd89e8644f39a6e3 | [
"Apache-2.0"
] | permissive | fpvandoorn/lean2 | 5a430a153b570bf70dc8526d06f18fc000a60ad9 | 0889cf65b7b3cebfb8831b8731d89c2453dd1e9f | refs/heads/master | 1,592,036,508,364 | 1,545,093,958,000 | 1,545,093,958,000 | 75,436,854 | 0 | 0 | null | 1,480,718,780,000 | 1,480,718,780,000 | null | UTF-8 | Lean | false | false | 2,923 | hlean | /-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
truncating an β-group to a group
-/
import hit.trunc algebra.bundled
open eq is_trunc trunc
namespace algebra
section
parameters (n : trunc_index) {A : Type... |
cdc1f7ea1c0a152d9bd1d798f181df48bdaeb551 | 874a8d2247ab9a4516052498f80da2e32d0e3a48 | /Stephanie.lean | 0481501079b6437845e46ddbc295bfc16269b185 | [] | no_license | AlexKontorovich/Spring2020Math492 | 378b36c643ee029f5ab91c1677889baa591f5e85 | 659108c5d864ff5c75b9b3b13b847aa5cff4348a | refs/heads/master | 1,610,780,595,457 | 1,588,174,859,000 | 1,588,174,859,000 | 243,017,788 | 0 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 3,907 | lean | import analysis.normed_space.basic
import topology.instances.ennreal
import analysis.normed_space.basic
import topology.instances.ennreal
import algebra.archimedean algebra.geom_sum
import data.nat.choose data.complex.basic
import tactic.linarith
import analysis.calculus.deriv
import data.complex.exponential
open fins... |
88ce79332cb50b2d5e439cde4f200700323e08b7 | c3f2fcd060adfa2ca29f924839d2d925e8f2c685 | /tests/lean/run/imp3.lean | 9fc586ce99fa525e95f72faa4f4534d64f4f4afb | [
"Apache-2.0"
] | permissive | respu/lean | 6582d19a2f2838a28ecd2b3c6f81c32d07b5341d | 8c76419c60b63d0d9f7bc04ebb0b99812d0ec654 | refs/heads/master | 1,610,882,451,231 | 1,427,747,084,000 | 1,427,747,429,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 235 | lean | structure is_equiv [class] {A B : Type} (f : A β B) :=
(inv : B β A)
check @is_equiv.inv
namespace is_equiv
context
parameters A B : Type
parameter f : A β B
parameter c : is_equiv f
check inv f
end
end is_equiv
|
56286c18ed463d3c555be124b6cfa827461b3f38 | 82b86ba2ae0d5aed0f01f49c46db5afec0eb2bd7 | /src/Lean/Data/LOption.lean | a79a3ffc27dfc97bd23fdc00b6053086c0067a78 | [
"Apache-2.0"
] | permissive | banksonian/lean4 | 3a2e6b0f1eb63aa56ff95b8d07b2f851072d54dc | 78da6b3aa2840693eea354a41e89fc5b212a5011 | refs/heads/master | 1,673,703,624,165 | 1,605,123,551,000 | 1,605,123,551,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,072 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
universes u
namespace Lean
inductive LOption (Ξ± : Type u)
| none : LOption Ξ±
| some : Ξ± β LOption Ξ±
| undef : LOption Ξ±
namespace LOption
variabl... |
6e31fc2d22f2f295f6bc9ffb541f5fb589e12d6f | bb31430994044506fa42fd667e2d556327e18dfe | /src/analysis/convex/basic.lean | 601c2623ecfe38c891953774a0ef8f14c6d2ba29 | [
"Apache-2.0"
] | permissive | sgouezel/mathlib | 0cb4e5335a2ba189fa7af96d83a377f83270e503 | 00638177efd1b2534fc5269363ebf42a7871df9a | refs/heads/master | 1,674,527,483,042 | 1,673,665,568,000 | 1,673,665,568,000 | 119,598,202 | 0 | 0 | null | 1,517,348,647,000 | 1,517,348,646,000 | null | UTF-8 | Lean | false | false | 21,769 | lean | /-
Copyright (c) 2019 Alexander Bentkamp. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp, Yury Kudriashov, YaΓ«l Dillies
-/
import algebra.order.module
import analysis.convex.star
import linear_algebra.affine_space.affine_subspace
/-!
# Convex sets a... |
3ce29020d77dac1508cc9ebf9707614c58f232c6 | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/ring_theory/roots_of_unity.lean | 65695bb8be27899764b67f0641563b24868b5521 | [
"Apache-2.0"
] | permissive | Lix0120/mathlib | 0020745240315ed0e517cbf32e738d8f9811dd80 | e14c37827456fc6707f31b4d1d16f1f3a3205e91 | refs/heads/master | 1,673,102,855,024 | 1,604,151,044,000 | 1,604,151,044,000 | 308,930,245 | 0 | 0 | Apache-2.0 | 1,604,164,710,000 | 1,604,163,547,000 | null | UTF-8 | Lean | false | false | 26,771 | lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import data.nat.parity
import data.polynomial.ring_division
import group_theory.order_of_element
import ring_theory.integral_domain
import number_theory.divisors
imp... |
200a9c6c1d1e7e68c2ef73dd8379ac5478bcd4d0 | 5756a081670ba9c1d1d3fca7bd47cb4e31beae66 | /Mathport/Syntax/Translate/Tactic/Mathlib/Choose.lean | b7f825c79bef8c4110eee126977d0023462ea8f4 | [
"Apache-2.0"
] | permissive | leanprover-community/mathport | 2c9bdc8292168febf59799efdc5451dbf0450d4a | 13051f68064f7638970d39a8fecaede68ffbf9e1 | refs/heads/master | 1,693,841,364,079 | 1,693,813,111,000 | 1,693,813,111,000 | 379,357,010 | 27 | 10 | Apache-2.0 | 1,691,309,132,000 | 1,624,384,521,000 | Lean | UTF-8 | Lean | false | false | 716 | lean | /-
Copyright (c) 2021 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathport.Syntax.Translate.Tactic.Basic
open Lean
open Lean.Elab.Tactic (Location)
namespace Mathport.Translate.Tactic
open AST3 Mathport.Translate.Par... |
a145f7590b05b9ea9992c1e387e04efb8d8a576b | 618003631150032a5676f229d13a079ac875ff77 | /src/category_theory/shift.lean | c64ab84628e558fee36118aa59886caf1de62c6f | [
"Apache-2.0"
] | permissive | awainverse/mathlib | 939b68c8486df66cfda64d327ad3d9165248c777 | ea76bd8f3ca0a8bf0a166a06a475b10663dec44a | refs/heads/master | 1,659,592,962,036 | 1,590,987,592,000 | 1,590,987,592,000 | 268,436,019 | 1 | 0 | Apache-2.0 | 1,590,990,500,000 | 1,590,990,500,000 | null | UTF-8 | Lean | false | false | 1,423 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.limits.shapes.zero
/-!
# Shift
A `shift` on a category is nothing more than an automorphism of the category. An example to
keep in mind might... |
6844f80ef038a3cb1f634ae360c5abc3e4ffca77 | 7bc35d4fbdda0c01e9b22a949940ee5cbb9800d0 | /manifold/field.lean | 981293f1b1850695dc5ce10a6699879103b00311 | [] | no_license | truonghoangle/manifolds | e6c2534dd46579f56ba99a48e2eb7ce51640e7c0 | dcf4815b29ad363ec9712fd00b7756c36cfa7c1c | refs/heads/main | 1,638,501,090,139 | 1,636,918,550,000 | 1,636,918,550,000 | 185,779,631 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,660 | lean | import analysis.normed_space.basic
import equiv
open set vector real
local attribute [instance] classical.prop_decidable
noncomputable theory
universes u v w x
variables {Ξ± : Type u} {Ξ² : Type v} {Ξ³ : Type w}
variables {n : β}
variable [normed_field Ξ±]
namespace Euclidean
instance :has_scalar Ξ± (Ξ ... |
ff1df575ac9b056672218a88188a00157513b9e0 | fecda8e6b848337561d6467a1e30cf23176d6ad0 | /src/data/finset/nat_antidiagonal.lean | d7f53446de384cfd171e7cc568c99131bc8e84e3 | [
"Apache-2.0"
] | permissive | spolu/mathlib | bacf18c3d2a561d00ecdc9413187729dd1f705ed | 480c92cdfe1cf3c2d083abded87e82162e8814f4 | refs/heads/master | 1,671,684,094,325 | 1,600,736,045,000 | 1,600,736,045,000 | 297,564,749 | 1 | 0 | null | 1,600,758,368,000 | 1,600,758,367,000 | null | UTF-8 | Lean | false | false | 2,077 | lean | /-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import data.finset.basic
import data.multiset.nat_antidiagonal
/-!
# The "antidiagonal" {(0,n), (1,n-1), ..., (n,0)} as a finset.
-/
namespace finset
namespace nat... |
2415b35f145f85ca19ee964ea7393c6f11132bc7 | 9be442d9ec2fcf442516ed6e9e1660aa9071b7bd | /stage0/src/Lean/Meta/Tactic/Simp.lean | 7f8fda529891399edc405082713f5e261866807d | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | EdAyers/lean4 | 57ac632d6b0789cb91fab2170e8c9e40441221bd | 37ba0df5841bde51dbc2329da81ac23d4f6a4de4 | refs/heads/master | 1,676,463,245,298 | 1,660,619,433,000 | 1,660,619,433,000 | 183,433,437 | 1 | 0 | Apache-2.0 | 1,657,612,672,000 | 1,556,196,574,000 | Lean | UTF-8 | Lean | false | false | 795 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Meta.Tactic.Simp.SimpTheorems
import Lean.Meta.Tactic.Simp.SimpCongrTheorems
import Lean.Meta.Tactic.Simp.Types
import Lean.Meta.Tactic.Simp.Mai... |
852ce962ff8e0748ff473791ea5e7c505d18db8c | 958488bc7f3c2044206e0358e56d7690b6ae696c | /lean/hhg/class.lean | 27113bf461d29b19c097b9b23cf094799c48485c | [] | no_license | possientis/Prog | a08eec1c1b121c2fd6c70a8ae89e2fbef952adb4 | d4b3debc37610a88e0dac3ac5914903604fd1d1f | refs/heads/master | 1,692,263,717,723 | 1,691,757,179,000 | 1,691,757,179,000 | 40,361,602 | 3 | 0 | null | 1,679,896,438,000 | 1,438,953,859,000 | Coq | UTF-8 | Lean | false | false | 64 | lean | @[class] structure inhabited2 (Ξ± : Type) :=
(default : Ξ±)
|
de59ba67a0b19d5d9e14e3b304756b10a33b9509 | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/category_theory/limits/shapes/types.lean | a45d55eccf9fb9c5b52124fbf57e8d7b66e93e38 | [
"Apache-2.0"
] | permissive | agjftucker/mathlib | d634cd0d5256b6325e3c55bb7fb2403548371707 | 87fe50de17b00af533f72a102d0adefe4a2285e8 | refs/heads/master | 1,625,378,131,941 | 1,599,166,526,000 | 1,599,166,526,000 | 160,748,509 | 0 | 0 | Apache-2.0 | 1,544,141,789,000 | 1,544,141,789,000 | null | UTF-8 | Lean | false | false | 7,245 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.limits.types
import category_theory.limits.shapes.products
import category_theory.limits.shapes.binary_products
import category_theory.limits.s... |
55a68d9bcf30870afe227f8c7a3b86cbbffad2e8 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/analysis/calculus/formal_multilinear_series.lean | 78aba40aa4ea60c0b8d40cc18bebdb9c9aeaec5b | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 12,462 | lean | /-
Copyright (c) 2019 SΓ©bastien GouΓ«zel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: SΓ©bastien GouΓ«zel
-/
import analysis.normed_space.multilinear
/-!
# Formal multilinear series
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corre... |
000a1d2c3f2f513bd8e4bf8f5f7f6c91a25821be | d1bbf1801b3dcb214451d48214589f511061da63 | /src/analysis/normed_space/operator_norm.lean | 2a4f9d93393f289f4bc575e51c8ce53126adb105 | [
"Apache-2.0"
] | permissive | cheraghchi/mathlib | 5c366f8c4f8e66973b60c37881889da8390cab86 | f29d1c3038422168fbbdb2526abf7c0ff13e86db | refs/heads/master | 1,676,577,831,283 | 1,610,894,638,000 | 1,610,894,638,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 45,040 | lean | /-
Copyright (c) 2019 Jan-David Salchow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jan-David Salchow, SΓ©bastien GouΓ«zel, Jean Lo
-/
import linear_algebra.finite_dimensional
import analysis.normed_space.riesz_lemma
import analysis.asymptotics
/-!
# Operator norm o... |
00538f4a241a4d15ebbb476f257f67f7949b7a03 | 618003631150032a5676f229d13a079ac875ff77 | /src/analysis/complex/basic.lean | 2d16172556db89c6de3dd6d544fd6e81613cf9dd | [
"Apache-2.0"
] | permissive | awainverse/mathlib | 939b68c8486df66cfda64d327ad3d9165248c777 | ea76bd8f3ca0a8bf0a166a06a475b10663dec44a | refs/heads/master | 1,659,592,962,036 | 1,590,987,592,000 | 1,590,987,592,000 | 268,436,019 | 1 | 0 | Apache-2.0 | 1,590,990,500,000 | 1,590,990,500,000 | null | UTF-8 | Lean | false | false | 8,405 | lean | /-
Copyright (c) SΓ©bastien GouΓ«zel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: SΓ©bastien GouΓ«zel
-/
import analysis.calculus.deriv
import analysis.normed_space.finite_dimension
/-!
# Normed space structure on `β`.
This file gathers basic facts on complex numbers ... |
b60af6a7e90c3e877564acf905415a5c1471aee6 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/instanceWhereDecls.lean | 24f4e080ef3f35b2078020374b28e7a9b6592939 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 321 | lean | inductive Foo where
| mk : Nat β Foo
| boo : String β Foo
instance : ToString Foo where
toString o := match o with
| .mk n => aux1 n
| .boo s => aux2 s
where
aux1 (n : Nat) : String :=
s!".mk {n}"
aux2 (s : String) : String :=
s!".boo {s}"
example : toString (Foo.mk 10) = ".mk 10" := rfl
|
899bab073b347c73ad9d1cc0acdbb5e6edc38038 | 6dc0c8ce7a76229dd81e73ed4474f15f88a9e294 | /stage0/src/Lean/Structure.lean | 4cda828ccbbebe2aa072b9e306df9d4a2bee018f | [
"Apache-2.0"
] | permissive | williamdemeo/lean4 | 72161c58fe65c3ad955d6a3050bb7d37c04c0d54 | 6d00fcf1d6d873e195f9220c668ef9c58e9c4a35 | refs/heads/master | 1,678,305,356,877 | 1,614,708,995,000 | 1,614,708,995,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,978 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
Helper functions for retrieving structure information.
-/
import Lean.Environment
import Lean.ProjFns
/- TODO: We currently assume that the projection functi... |
45387406b68c7e1f213a993c4d1e068367358b3b | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/data/equiv/encodable/lattice.lean | c4370eb66d8ff6c5bd9c529c9bbce483772467ae | [
"Apache-2.0"
] | permissive | abentkamp/mathlib | d9a75d291ec09f4637b0f30cc3880ffb07549ee5 | 5360e476391508e092b5a1e5210bd0ed22dc0755 | refs/heads/master | 1,682,382,954,948 | 1,622,106,077,000 | 1,622,106,077,000 | 149,285,665 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,943 | lean | /-
Copyright (c) 2020 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
import data.equiv.encodable.basic
import data.finset.basic
import data.set.disjointed
/-!
# Lattice operations on encodable types
Lemmas about lattice and set op... |
0742cf0d27f39116e1d3e539c41d939c9f6b0c86 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/topology/uniform_space/completion.lean | bdc3787f9414355c17138c86fe1f2052f0311053 | [
"Apache-2.0"
] | permissive | AntoineChambert-Loir/mathlib | 64aabb896129885f12296a799818061bc90da1ff | 07be904260ab6e36a5769680b6012f03a4727134 | refs/heads/master | 1,693,187,631,771 | 1,636,719,886,000 | 1,636,719,886,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 23,235 | lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes HΓΆlzl
-/
import topology.uniform_space.abstract_completion
/-!
# Hausdorff completions of uniform spaces
The goal is to construct a left-adjoint to the inclu... |
61843902e589979cb77f3a9bba3cd4c6d3090b46 | 56e5b79a7ab4f2c52e6eb94f76d8100a25273cf3 | /src/tests/test_timing.lean | 76a48453e6da78668ad6f809b48e43e241b80403 | [
"Apache-2.0"
] | permissive | DyeKuu/lean-tpe-public | 3a9968f286ca182723ef7e7d97e155d8cb6b1e70 | 750ade767ab28037e80b7a80360d213a875038f8 | refs/heads/master | 1,682,842,633,115 | 1,621,330,793,000 | 1,621,330,793,000 | 368,475,816 | 0 | 0 | Apache-2.0 | 1,621,330,745,000 | 1,621,330,744,000 | null | UTF-8 | Lean | false | false | 282 | lean | import system.io
import tactic
meta def main : tactic unit := do {
tactic.try_for_time 5000 $ do {
([1,2,3,4,5,6,7,8,9,10] : list β).mmap' (Ξ» k, tactic.try_for_time 1000 $ do {
tactic.sleep (250 * k),
tactic.trace format!"NUM: {k}"
})
}
}
-- #eval main
|
adc89387efd1a22be056edd892ee53e44a9badae | 5d166a16ae129621cb54ca9dde86c275d7d2b483 | /library/init/algebra/ordered_field.lean | a0b7ac81c608c35473c129e397e4d4a057cc4d99 | [
"Apache-2.0"
] | permissive | jcarlson23/lean | b00098763291397e0ac76b37a2dd96bc013bd247 | 8de88701247f54d325edd46c0eed57aeacb64baf | refs/heads/master | 1,611,571,813,719 | 1,497,020,963,000 | 1,497,021,515,000 | 93,882,536 | 1 | 0 | null | 1,497,029,896,000 | 1,497,029,896,000 | null | UTF-8 | Lean | false | false | 19,486 | lean | /-
Copyright (c) 2014 Robert Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Lewis, Leonardo de Moura
-/
prelude
import init.algebra.ordered_ring init.algebra.field
set_option old_structure_cmd true
universe u
class linear_ordered_field (Ξ± : Type u) ext... |
6ab797b07eec310e027d8ee0e0647e960ef21ada | 33340b3a23ca62ef3c8a7f6a2d4e14c07c6d3354 | /dlo/basic.lean | 7ee468799a8c94f067ab8e97811c1d91b59f894f | [] | no_license | lclem/cooper | 79554e72ced343c64fed24b2d892d24bf9447dfe | 812afc6b158821f2e7dac9c91d3b6123c7a19faf | refs/heads/master | 1,607,554,257,488 | 1,578,694,133,000 | 1,578,694,133,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,603 | lean | import .formula ..logic
def dep_0 : atom_dlo β Prop
| (t1 =' t2) := t1 = V' 0 β¨ t2 = V' 0
| (t1 <' t2) := t1 = V' 0 β¨ t2 = V' 0
instance dec_dep_0 : decidable_pred dep_0
| (x <' y) := begin simp [dep_0], apply_instance end
| (x =' y) := begin simp [dep_0], apply_instance end
def solv_0 : atom_dlo β Prop
| (t1 <' ... |
f005500f106039c0cb5807e2ed49122dabcff916 | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /tmp/Basic.lean | bf4521d7564e3f8b1828c6c5be36818a73a6695f | [
"Apache-2.0"
] | permissive | mhuisi/lean4 | 28d35a4febc2e251c7f05492e13f3b05d6f9b7af | dda44bc47f3e5d024508060dac2bcb59fd12e4c0 | refs/heads/master | 1,621,225,489,283 | 1,585,142,689,000 | 1,585,142,689,000 | 250,590,438 | 0 | 2 | Apache-2.0 | 1,602,443,220,000 | 1,585,327,814,000 | C | UTF-8 | Lean | false | false | 17,604 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Sebastian Ullrich
-/
prelude
import Init.Control.Reader
import Init.Lean.Meta
import Init.Lean.Parser.Module
namespace Lean
namespace Elab
/-
structure Elab... |
ca7d94b4c307c0c8496162182adbe2dec995edd3 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/analysis/normed_space/continuous_linear_map.lean | 1ca9737ceac0aa7d2ba725dbe180e1855db6c5b8 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 10,780 | lean | /-
Copyright (c) 2019 Jan-David Salchow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jan-David Salchow, SΓ©bastien GouΓ«zel, Jean Lo
-/
import analysis.normed_space.basic
/-! # Constructions of continuous linear maps between (semi-)normed spaces
> THIS FILE IS SYNCH... |
261e65a882bbd03c1eab7028e88c2374bc8ce4ea | 626e312b5c1cb2d88fca108f5933076012633192 | /src/algebra/algebra/subalgebra.lean | 195b6d60d0305eff783a702529703cd79608d445 | [
"Apache-2.0"
] | permissive | Bioye97/mathlib | 9db2f9ee54418d29dd06996279ba9dc874fd6beb | 782a20a27ee83b523f801ff34efb1a9557085019 | refs/heads/master | 1,690,305,956,488 | 1,631,067,774,000 | 1,631,067,774,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 31,131 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Yury Kudryashov
-/
import algebra.algebra.operations
/-!
# Subalgebras over Commutative Semiring
In this file we define `subalgebra`s and the usual operations on them (`map`, `... |
d03bba559ec0cd639494d44a02c173b25c658fef | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/data/nat/sqrt.lean | f5e2cd0bc455ca4fb9b484f80b0d3c438d80d9d5 | [
"Apache-2.0"
] | permissive | fpvandoorn/mathlib | b21ab4068db079cbb8590b58fda9cc4bc1f35df4 | b3433a51ea8bc07c4159c1073838fc0ee9b8f227 | refs/heads/master | 1,624,791,089,608 | 1,556,715,231,000 | 1,556,715,231,000 | 165,722,980 | 5 | 0 | Apache-2.0 | 1,552,657,455,000 | 1,547,494,646,000 | Lean | UTF-8 | Lean | false | false | 6,962 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Johannes HΓΆlzl, Mario Carneiro
An efficient binary implementation of a (sqrt n) function that
returns s s.t.
s*s β€ n β€ s*s + s + s
-/
import data.nat.bas... |
2e908d98827ee3c2d9845cb40860532c1efe5ed0 | 649957717d58c43b5d8d200da34bf374293fe739 | /src/topology/uniform_space/completion.lean | 25b3699019df68997f3d3f473a6a3c9faf40b23f | [
"Apache-2.0"
] | permissive | Vtec234/mathlib | b50c7b21edea438df7497e5ed6a45f61527f0370 | fb1848bbbfce46152f58e219dc0712f3289d2b20 | refs/heads/master | 1,592,463,095,113 | 1,562,737,749,000 | 1,562,737,749,000 | 196,202,858 | 0 | 0 | Apache-2.0 | 1,562,762,338,000 | 1,562,762,337,000 | null | UTF-8 | Lean | false | false | 26,408 | lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes HΓΆlzl
Hausdorff completions of uniform spaces.
The goal is to construct a left-adjoint to the inclusion of complete Hausdorff uniform spaces
into all uniform... |
c9f054a4aad392767ecaf4b190f4348514c610c3 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/geometry/manifold/algebra/structures.lean | e90599f0c066de2a2756c2a9918ca3d53cefdac7 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 2,742 | lean | /-
Copyright Β© 2020 NicolΓ² Cavalleri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: NicolΓ² Cavalleri
-/
import geometry.manifold.algebra.lie_group
/-!
# Smooth structures
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding P... |
63eef713606d734a88ae3f4c344a3a795a24a916 | 74caf7451c921a8d5ab9c6e2b828c9d0a35aae95 | /library/init/meta/simp_tactic.lean | 8c6d936d7180ffc5282ecadaa1422292064e07ec | [
"Apache-2.0"
] | permissive | sakas--/lean | f37b6fad4fd4206f2891b89f0f8135f57921fc3f | 570d9052820be1d6442a5cc58ece37397f8a9e4c | refs/heads/master | 1,586,127,145,194 | 1,480,960,018,000 | 1,480,960,635,000 | 40,137,176 | 0 | 0 | null | 1,438,621,351,000 | 1,438,621,351,000 | null | UTF-8 | Lean | false | false | 12,677 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.meta.tactic init.meta.attribute init.meta.constructor_tactic
import init.meta.relation_tactics init.meta.occurrences
open tactic
meta ... |
debf7c0a3220649f4d1fc2fa5c9fea23dfff6f6b | 5a8eb1c11f93715e070b588e85f2961065c3714d | /books/theorem-proving-in-lean/ch02-06-2.lean | 48266e9863683f18596a0fd500f04d1a0f360d6b | [
"MIT"
] | permissive | luksamuk/study | 0e19bf99d33e0793127c3d3f8ad3936fbeb36505 | 6a9417e071a8624c4cd9db696c16a3abcc430219 | refs/heads/master | 1,677,960,533,266 | 1,676,234,529,000 | 1,676,234,529,000 | 151,009,060 | 4 | 1 | MIT | 1,676,234,531,000 | 1,538,343,224,000 | C++ | UTF-8 | Lean | false | false | 270 | lean | section useful
variables (Ξ± Ξ² Ξ³ : Type)
variables (g : Ξ² β Ξ³) (f : Ξ± β Ξ²) (h : Ξ± β Ξ±)
variable x : Ξ±
def compose := g (f x)
def do_twice := h (h x)
def do_thrice := h (h (h x))
end useful
#print compose
#print do_twice
#print do_thrice
|
1d99cc1fd1d413e3a99d678c917baa8e230ce08f | f3a5af2927397cf346ec0e24312bfff077f00425 | /src/game/world10/level12.lean | 850dcb740f1c856e5eb14c982f9e6ab361de23fc | [
"Apache-2.0"
] | permissive | ImperialCollegeLondon/natural_number_game | 05c39e1586408cfb563d1a12e1085a90726ab655 | f29b6c2884299fc63fdfc81ae5d7daaa3219f9fd | refs/heads/master | 1,688,570,964,990 | 1,636,908,242,000 | 1,636,908,242,000 | 195,403,790 | 277 | 84 | Apache-2.0 | 1,694,547,955,000 | 1,562,328,792,000 | Lean | UTF-8 | Lean | false | false | 446 | lean | import game.world10.level11 -- hide
namespace mynat -- hide
/-
# Inequality world.
## Level 12: `le_of_succ_le_succ`
-/
/- Lemma
For all naturals $a$ and $b$,
$\operatorname{succ}(a)\le\operatorname{succ}(b)\implies a\le b.$
-/
theorem le_of_succ_le_succ (a b : mynat) : succ a β€ succ b β a β€ b :=
begin [nat_num_g... |
8ea8f972139b479bb253451b6bfebd432d5b464e | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/set_theory/ordinal/notation.lean | 1e06926c5a76a82ca8ad24c2aab96374e74f525b | [
"Apache-2.0"
] | permissive | jcommelin/mathlib | d8456447c36c176e14d96d9e76f39841f69d2d9b | ee8279351a2e434c2852345c51b728d22af5a156 | refs/heads/master | 1,664,782,136,488 | 1,663,638,983,000 | 1,663,638,983,000 | 132,563,656 | 0 | 0 | Apache-2.0 | 1,663,599,929,000 | 1,525,760,539,000 | Lean | UTF-8 | Lean | false | false | 45,036 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import set_theory.ordinal.principal
/-!
# Ordinal notation
Constructive ordinal arithmetic for ordinals below `Ξ΅β`.
We define a type `onote`, with constructors `0... |
d7fb8c714680b35290f00a6e7a7c3563a104a359 | 32025d5c2d6e33ad3b6dd8a3c91e1e838066a7f7 | /tests/lean/Process.lean | 50e21f71fa679dc70289a7cf89b72720b9bdc543 | [
"Apache-2.0"
] | permissive | walterhu1015/lean4 | b2c71b688975177402758924eaa513475ed6ce72 | 2214d81e84646a905d0b20b032c89caf89c737ad | refs/heads/master | 1,671,342,096,906 | 1,599,695,985,000 | 1,599,695,985,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 702 | lean | open IO.Process
#eval do
child β spawn { cmd := "sh", args := #["-c", "exit 1"] };
child.wait
#eval do
child β spawn { cmd := "sh", args := #["-c", "echo hi!"] };
child.wait
#eval do
child β spawn { cmd := "sh", args := #["-c", "echo ho!"], stdout := Stdio.piped };
child.wait;
child.stdout.readToEnd
#... |
2e56d7d33353be607a946061943676520de784bb | 367134ba5a65885e863bdc4507601606690974c1 | /src/analysis/analytic/basic.lean | 92c3ea3d40bea70d8264c91a112940fc3c6c2953 | [
"Apache-2.0"
] | permissive | kodyvajjha/mathlib | 9bead00e90f68269a313f45f5561766cfd8d5cad | b98af5dd79e13a38d84438b850a2e8858ec21284 | refs/heads/master | 1,624,350,366,310 | 1,615,563,062,000 | 1,615,563,062,000 | 162,666,963 | 0 | 0 | Apache-2.0 | 1,545,367,651,000 | 1,545,367,651,000 | null | UTF-8 | Lean | false | false | 47,252 | lean | /-
Copyright (c) 2020 SΓ©bastien GouΓ«zel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: SΓ©bastien GouΓ«zel, Yury Kudryashov
-/
import analysis.calculus.formal_multilinear_series
import analysis.specific_limits
/-!
# Analytic functions
A function is analytic in one dim... |
5b45122c4040e1d2d163a943cddccbf2eb1b2dfa | bb31430994044506fa42fd667e2d556327e18dfe | /src/topology/metric_space/gromov_hausdorff_realized.lean | c8bf97b84234c92f43e9138f516930ed570dfc4f | [
"Apache-2.0"
] | permissive | sgouezel/mathlib | 0cb4e5335a2ba189fa7af96d83a377f83270e503 | 00638177efd1b2534fc5269363ebf42a7871df9a | refs/heads/master | 1,674,527,483,042 | 1,673,665,568,000 | 1,673,665,568,000 | 119,598,202 | 0 | 0 | null | 1,517,348,647,000 | 1,517,348,646,000 | null | UTF-8 | Lean | false | false | 27,343 | lean | /-
Copyright (c) 2019 SΓ©bastien GouΓ«zel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: SΓ©bastien GouΓ«zel
-/
import topology.metric_space.gluing
import topology.metric_space.hausdorff_distance
import topology.continuous_function.bounded
/-!
# The Gromov-Hausdorff dist... |
be17741e95c291f050cc5df2b5840910af2164ee | 8c02fed42525b65813b55c064afe2484758d6d09 | /src/spec/lemmas_basic.lean | ce51598716fc80df4872503cdb413a72dbe84425 | [
"LicenseRef-scancode-generic-cla",
"MIT"
] | permissive | microsoft/AliveInLean | 3eac351a34154efedd3ffc4fe2fa4ec01b219e0d | 4b739dd6e4266b26a045613849df221374119871 | refs/heads/master | 1,691,419,737,939 | 1,689,365,567,000 | 1,689,365,568,000 | 131,156,103 | 23 | 18 | NOASSERTION | 1,660,342,040,000 | 1,524,747,538,000 | Lean | UTF-8 | Lean | false | false | 8,062 | lean | -- Copyright (c) Microsoft Corporation. All rights reserved.
-- Licensed under the MIT license.
universes u v
-- Basic
lemma prod_inj: β {Ξ±:Type u} {Ξ²:Type v} (p q:Ξ± Γ Ξ²),
p = q β p.fst = q.fst β§ p.snd = q.snd
:= begin
intros,
split,
{ intros H, rw H, split; refl },
{ intros H, cases p, cases q, simp at H,
... |
ad00cce799ead0d3af338bd31a8dc929c2bb4907 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/const_choice.lean | bcf1f3373a482d037ae711be61c37a3b7f0e1e2d | [
"Apache-2.0"
] | permissive | leanprover-community/lean | 12b87f69d92e614daea8bcc9d4de9a9ace089d0e | cce7990ea86a78bdb383e38ed7f9b5ba93c60ce0 | refs/heads/master | 1,687,508,156,644 | 1,684,951,104,000 | 1,684,951,104,000 | 169,960,991 | 457 | 107 | Apache-2.0 | 1,686,744,372,000 | 1,549,790,268,000 | C++ | UTF-8 | Lean | false | false | 116 | lean | open nat
definition mypred (a : nat) : nat :=
nat.cases_on a
0
(fun aβ, aβ)
example : mypred 1 = 0 :=
rfl
|
c04de7fa68272208bd3793d2863bb486fb298609 | aa5a655c05e5359a70646b7154e7cac59f0b4132 | /src/Lean/Data/Lsp/LanguageFeatures.lean | c48d3b0fa3e6d1c20a80177b174374025e477ccd | [
"Apache-2.0"
] | permissive | lambdaxymox/lean4 | ae943c960a42247e06eff25c35338268d07454cb | 278d47c77270664ef29715faab467feac8a0f446 | refs/heads/master | 1,677,891,867,340 | 1,612,500,005,000 | 1,612,500,005,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,714 | lean | /-
Copyright (c) 2020 Wojciech Nawrocki. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wojciech Nawrocki
-/
import Lean.Data.Json
import Lean.Data.Lsp.Basic
namespace Lean
namespace Lsp
open Json
structure Hover where
/- NOTE we should also accept MarkedString/M... |
0a3841dde2664a05fc0e06cf6207f2022e035ddd | 206422fb9edabf63def0ed2aa3f489150fb09ccb | /src/ring_theory/roots_of_unity.lean | d8075fc63b3ffdd4c0df71c9f75c002bf78c5246 | [
"Apache-2.0"
] | permissive | hamdysalah1/mathlib | b915f86b2503feeae268de369f1b16932321f097 | 95454452f6b3569bf967d35aab8d852b1ddf8017 | refs/heads/master | 1,677,154,116,545 | 1,611,797,994,000 | 1,611,797,994,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 38,007 | lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import data.nat.parity
import data.polynomial.ring_division
import group_theory.order_of_element
import ring_theory.integral_domain
import number_theory.divisors
imp... |
9e0a2e8144f800336de028fe1a0ac7d625491f59 | cc62cd292c1acc80a10b1c645915b70d2cdee661 | /src/category_theory/functor/isomorphism.lean | 2c3f952fe28770e0871ad46fddd7e1809f9599c9 | [] | no_license | RitaAhmadi/lean-category-theory | 4afb881c4b387ee2c8ce706c454fbf9db8897a29 | a27b4ae5eac978e9188d2e867c3d11d9a5b87a9e | refs/heads/master | 1,651,786,183,402 | 1,565,604,314,000 | 1,565,604,314,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 864 | lean | -- Copyright (c) 2018 Scott Morrison. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Scott Morrison
import category_theory.fully_faithful
open category_theory
namespace category_theory
universes vβ vβ uβ uβ
variables {C : Type uβ} [π : category.{vβ} C] {D :... |
fa2fe11bba7b05dadc80173d4899a41d26356ce8 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/tactic/nth_rewrite/congr.lean | be250f5716b6b7039004d5fb335483a4ce9174bd | [
"Apache-2.0"
] | permissive | jjgarzella/mathlib | 96a345378c4e0bf26cf604aed84f90329e4896a2 | 395d8716c3ad03747059d482090e2bb97db612c8 | refs/heads/master | 1,686,480,124,379 | 1,625,163,323,000 | 1,625,163,323,000 | 281,190,421 | 2 | 0 | Apache-2.0 | 1,595,268,170,000 | 1,595,268,169,000 | null | UTF-8 | Lean | false | false | 3,198 | lean | /-
Copyright (c) 2018 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Keeley Hoek, Scott Morrison
-/
import tactic.nth_rewrite.basic
import tactic.core
import data.mllist
namespace tactic
namespace nth_rewrite.congr
open nth_rewrite
/-- Helper functi... |
b94bd1e7673164c0664e2038f79f1b4aab3f8500 | ff5230333a701471f46c57e8c115a073ebaaa448 | /library/init/data/list/basic.lean | 6dc8af4f56ad0c747bab112a4df5aab9fbe9331d | [
"Apache-2.0"
] | permissive | stanford-cs242/lean | f81721d2b5d00bc175f2e58c57b710d465e6c858 | 7bd861261f4a37326dcf8d7a17f1f1f330e4548c | refs/heads/master | 1,600,957,431,849 | 1,576,465,093,000 | 1,576,465,093,000 | 225,779,423 | 0 | 3 | Apache-2.0 | 1,575,433,936,000 | 1,575,433,935,000 | null | UTF-8 | Lean | false | false | 10,111 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
prelude
import init.logic init.data.nat.basic init.data.bool.basic init.propext
open decidable list
universes u v w
instance (Ξ± : Type u) : inhabited (list... |
2bf9fd77b71065434ec65e7ea859532579d60781 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/simp_univ_poly.lean | 63a7aebc90f5b5b0b151de9ac3375578e28d0ee1 | [
"Apache-2.0"
] | permissive | leanprover-community/lean | 12b87f69d92e614daea8bcc9d4de9a9ace089d0e | cce7990ea86a78bdb383e38ed7f9b5ba93c60ce0 | refs/heads/master | 1,687,508,156,644 | 1,684,951,104,000 | 1,684,951,104,000 | 169,960,991 | 457 | 107 | Apache-2.0 | 1,686,744,372,000 | 1,549,790,268,000 | C++ | UTF-8 | Lean | false | false | 809 | lean | namespace test
universes u v
def equinumerous (Ξ± : Type u) (Ξ² : Type v) :=
β f : Ξ± β Ξ², function.bijective f
local infix (name := equiv) ` β `:50 := equinumerous
@[refl] lemma refl {Ξ±} : Ξ± β Ξ± := sorry
@[trans] lemma trans {Ξ± Ξ² Ξ³} :
Ξ± β Ξ² β Ξ² β Ξ³ β Ξ± β Ξ³ := sorry
@[congr] lemma equinumerous.congr_eqn {Ξ± Ξ±' Ξ² Ξ²'... |
2676380fc805537eaa0c7f3f137279e5f2ff22cb | 32025d5c2d6e33ad3b6dd8a3c91e1e838066a7f7 | /tests/lean/run/typeclass_append.lean | c0e1452ababa539a9bf9fb7eee844cd15c66e504 | [
"Apache-2.0"
] | permissive | walterhu1015/lean4 | b2c71b688975177402758924eaa513475ed6ce72 | 2214d81e84646a905d0b20b032c89caf89c737ad | refs/heads/master | 1,671,342,096,906 | 1,599,695,985,000 | 1,599,695,985,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,467 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Daniel Selsam
Performance test to ensure quadratic blowup is avoided.
-/
class Append {Ξ± : Type} (xsβ xsβ : List Ξ±) (out : outParam $ List Ξ±) : Type :=
(u : Unit := ())
instan... |
0aeca0b3fd71ca9910c5ac965ced1daac512ca06 | d436468d80b739ba7e06843c4d0d2070e43448e5 | /src/measure_theory/measurable_space.lean | 8e51617bdfb6f0fb60705e49fb0940c4505de41d | [
"Apache-2.0"
] | permissive | roro47/mathlib | 761fdc002aef92f77818f3fef06bf6ec6fc1a28e | 80aa7d52537571a2ca62a3fdf71c9533a09422cf | refs/heads/master | 1,599,656,410,625 | 1,573,649,488,000 | 1,573,649,488,000 | 221,452,951 | 0 | 0 | Apache-2.0 | 1,573,647,693,000 | 1,573,647,692,000 | null | UTF-8 | Lean | false | false | 42,851 | lean | /-
Copyright (c) 2017 Johannes HΓΆlzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes HΓΆlzl, Mario Carneiro
Measurable spaces -- Ο-algberas
-/
import data.set.disjointed order.galois_connection data.set.countable
/-!
# Measurable spaces and measurable functio... |
f18c49ecbbf6e28ea343e4a5449c149ac7a4345b | ae1e94c332e17c7dc7051ce976d5a9eebe7ab8a5 | /src/Lean/Elab/Binders.lean | df46b64a2f8f7d08af304aa21c0e896c2758e338 | [
"Apache-2.0"
] | permissive | dupuisf/lean4 | d082d13b01243e1de29ae680eefb476961221eef | 6a39c65bd28eb0e28c3870188f348c8914502718 | refs/heads/master | 1,676,948,755,391 | 1,610,665,114,000 | 1,610,665,114,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 24,334 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Elab.Term
import Lean.Parser.Term
namespace Lean.Elab.Term
open Meta
open Lean.Parser.Term
/--
Given syntax of the forms
a) (`:` term)?
... |
0cb5f5b107d019ee623d2ed6e5ebe8470d786a22 | 6d50885e7b3f72447a03f21d5268d6af87c0a404 | /answers/natural deduction.lean | 71d9aabd9e3194b364ae83dfd6d7dc22a0231861 | [] | no_license | kevinsullivan/uva-cs-dm-s20-old | 583c756cded281fcee7f1afc42cb3e08f89c2493 | 797672cb0ffae6a42a3518c9225d5807191fd113 | refs/heads/master | 1,607,500,914,982 | 1,578,752,991,000 | 1,578,752,991,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 14,907 | lean | /-
An axiom is an assumed proof of a
given proposition. For example, we
accept as an *axiom* that there is
a proof that equality is reflexive.
refl : β {Ξ± : Type} (a : Ξ±), a = a.
Natural deduction is a system of
reasoning rules for deducing proofs
of more complex propositions from
axioms.
What we are doing in class ... |
ee8ea8bffa494e7ef80caa2fc1f44beffc579caf | fd3506535396cef3d1bdcf4ae5b87c8ed9ff2c2e | /migrated/bigops.lean | a7b0622c1b771282a3274fca7d3c719d936d4bc6 | [] | no_license | williamdemeo/leanproved | 77933dbcb8bfbae61a753ae31fa669b3ed8cda9d | d8c2e2ca0002b252fce049c4ff9be0e9e83a6374 | refs/heads/master | 1,598,674,802,432 | 1,437,528,488,000 | 1,437,528,488,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,164 | lean | /-
Copyright (c) 2015 Haitao Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author : Haitao Zhang
-/
import algebra.group_bigops algebra.group_power
open nat algebra function binary quot subtype list finset
namespace migration
section group
lemma Prodl_singleton {A B... |
b9531a53eb344faddcec289e8ee2a785877a8331 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /src/Init/Data/UInt.lean | 9eba26f9db603078346badc9264ce70c66772812 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 217 | lean | /-
Copyright (c) 2022 Henrik BΓΆving. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Henrik BΓΆving
-/
prelude
import Init.Data.UInt.Basic
import Init.Data.UInt.Log2
|
43b01a4a36cc27b119cdea3d8ba78d15b0da4cf5 | 8e381650eb2c1c5361be64ff97e47d956bf2ab9f | /src/to_mathlib/localization/localization_alt.lean | a70773cbdfbdbe02255cfc5630f5e25278965b9f | [] | no_license | alreadydone/lean-scheme | 04c51ab08eca7ccf6c21344d45d202780fa667af | 52d7624f57415eea27ed4dfa916cd94189221a1c | refs/heads/master | 1,599,418,221,423 | 1,562,248,559,000 | 1,562,248,559,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,598 | lean | /-
The localization predicate (by Neil Strickland).
This is Kenny's refactoring of the originial code taken from:
https://github.com/kckennylau/Lean/blob/master/localization_alt.lean
-/
import algebra.ring
import group_theory.submonoid
import ring_theory.ideal_operations
import linear_algebra.basic
import to_m... |
cd96f310660b7e4e0d783cb9f84494ed4ca2e704 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/algebra/associated.lean | f27c8be38caae0440475df93e55815f90c466364 | [
"Apache-2.0"
] | permissive | jcommelin/mathlib | d8456447c36c176e14d96d9e76f39841f69d2d9b | ee8279351a2e434c2852345c51b728d22af5a156 | refs/heads/master | 1,664,782,136,488 | 1,663,638,983,000 | 1,663,638,983,000 | 132,563,656 | 0 | 0 | Apache-2.0 | 1,663,599,929,000 | 1,525,760,539,000 | Lean | UTF-8 | Lean | false | false | 39,285 | lean | /-
Copyright (c) 2018 Johannes HΓΆlzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes HΓΆlzl, Jens Wagemaker
-/
import algebra.divisibility
import algebra.group_power.lemmas
import algebra.invertible
import order.atoms
/-!
# Associated, prime, and irreducible e... |
5fddf56544f6e11c8d4434f214144e136d6e606f | e21db629d2e37a833531fdcb0b37ce4d71825408 | /alt/untyped.lean | 4c40c9f7cbf00558efeb3a24ac9f548a8ddb6876 | [] | no_license | fischerman/GPU-transformation-verifier | 614a28cb4606a05a0eb27e8d4eab999f4f5ea60c | 75a5016f05382738ff93ce5859c4cfa47ccb63c1 | refs/heads/master | 1,586,985,789,300 | 1,579,290,514,000 | 1,579,290,514,000 | 165,031,073 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,535 | lean | import data.set.basic
import data.list
import logic.relator
#check list.forallβ
namespace MCL_untyped
inductive type
| int
| float
open type
instance : decidable_eq type := sorry
@[reducible]
def type_map : type β Type
| int := β
| float := β
prefix βΈ := type_map
@[reducible]
def untyped_value := β
@[reducible... |
c2374514e8c1f31c6aec98ac5d0d20c3a5a0002a | 4bcaca5dc83d49803f72b7b5920b75b6e7d9de2d | /src/Lean/Util/Path.lean | 89400a8a513dd7350a912d29969e1754dc0764b6 | [
"Apache-2.0"
] | permissive | subfish-zhou/leanprover-zh_CN.github.io | 30b9fba9bd790720bd95764e61ae796697d2f603 | 8b2985d4a3d458ceda9361ac454c28168d920d3f | refs/heads/master | 1,689,709,967,820 | 1,632,503,056,000 | 1,632,503,056,000 | 409,962,097 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,118 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Sebastian Ullrich
Management of the Lean search path (`LEAN_PATH`), which is a list of
paths containing package roots: an import `A.B.C` resolves to
`path/A/... |
02746c4624edaf11b82a7c76f75f1d03e76eb019 | c17c60327eee1622a8d7defa5af340e08619107f | /src/snippets/tactics/structures.lean | 9455790fe34c44e828fa24ddee4823b52c1f0e50 | [] | no_license | FredericLeRoux/dEAduction-lean2 | 277e3aad5102ff155fb04b188dbd01568ceea005 | bf7d7d88c2511ecfda5a98ed96e4ca3bc7ae1151 | refs/heads/master | 1,667,931,697,036 | 1,593,174,880,000 | 1,593,174,880,000 | 275,150,842 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 19,054 | lean | import data.real.basic
import data.set
import tactic
open push_neg
namespace tactic.interactive
open lean.parser tactic interactive
open interactive (loc.ns)
open interactive.types
open tactic expr
local postfix *:9001 := many -- sinon ne comprends pas ident*
/- décompose en premier caractère, reste INUTILISE-/
d... |
a5c736334a702d37138299e3b5b49aab81c1e57d | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/elabissues/bind_with_existential_types.lean | 9150073133ccd3291196cee5ab1ec352ce7d5ae2 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 1,557 | lean | /-
Problem: existential types do not play well with monads.
```
class Bind (m : Type u β Type v) :=
(bind : β {Ξ± Ξ² : Type u}, m Ξ± β (Ξ± β m Ξ²) β m Ξ²)
```
Even if we fix a universe-polymorphic monad M.{u v} : Type u -> Type v,
the bind operator forces the universes of the two applications of M to be the same.
So, we ca... |
76e75d47623d02cfbf3686f6848b9cd4079424eb | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/bubble.lean | 497a904c93d1489a191eb4533937f8656f9d9893 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 588 | lean | def List.bubblesort [LT Ξ±] [DecidableRel (Β· < Β· : Ξ± β Ξ± β Prop)] (l : List Ξ±) : {l' : List Ξ± // l.length = l'.length} :=
match l with
| [] => β¨[], rflβ©
| x :: xs =>
match bubblesort xs with
| β¨[], hβ© => β¨[x], by simp[h]β©
| β¨y :: ys, hβ© =>
if y < x then
have : Nat.succ (length ys) < Nat.s... |
58c0bb8da95fbeb191697c79aff15f99a52ee19b | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/field_theory/finite_card.lean | d6058b3e5a6ef67f67baa27014341e41d01713ce | [
"Apache-2.0"
] | permissive | fpvandoorn/mathlib | b21ab4068db079cbb8590b58fda9cc4bc1f35df4 | b3433a51ea8bc07c4159c1073838fc0ee9b8f227 | refs/heads/master | 1,624,791,089,608 | 1,556,715,231,000 | 1,556,715,231,000 | 165,722,980 | 5 | 0 | Apache-2.0 | 1,552,657,455,000 | 1,547,494,646,000 | Lean | UTF-8 | Lean | false | false | 1,116 | lean | /-
Copyright (c) 2019 Casper Putz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joey van Langen, Casper Putz
-/
import algebra.char_p data.zmod.basic linear_algebra.basis
universes u
variables (Ξ± : Type u) [discrete_field Ξ±] [fintype Ξ±]
namespace finite_field
the... |
0ecdf4adcd79a0bf17243a0290eca5a6bb0838a0 | 6b45072eb2b3db3ecaace2a7a0241ce81f815787 | /algebra/lattice/complete_lattice.lean | d654149972efb30755d345150bd0d5992aab6a9a | [] | no_license | avigad/library_dev | 27b47257382667b5eb7e6476c4f5b0d685dd3ddc | 9d8ac7c7798ca550874e90fed585caad030bbfac | refs/heads/master | 1,610,452,468,791 | 1,500,712,839,000 | 1,500,713,478,000 | 69,311,142 | 1 | 0 | null | 1,474,942,903,000 | 1,474,942,902,000 | null | UTF-8 | Lean | false | false | 20,250 | lean | /-
Copyright (c) 2017 Johannes HΓΆlzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes HΓΆlzl
Theory of complete lattices.
-/
import .bounded_lattice
set_option old_structure_cmd true
universes u v w wβ
variables {Ξ± : Type u} {Ξ² : Type v} {ΞΉ : Sort w} {ΞΉβ : So... |
7b74feac566c4a866bd63b09b3545ebf86943d76 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/441.lean | 524b0840ed80ed3cbbf18aa179536a969a0a9cdd | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 115 | lean | theorem ex (v v' : Nat) (ty : Nat β String) (h : some v = some v') : some (ty v) = some (ty v') := by
simp_all
|
9d8fa9d0bbd7cb3fb4e3557e0e6583638c3d5de3 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/algebra/group/basic.lean | d32cc6b0cf65015a350191acc848f1ff8f2239d3 | [
"Apache-2.0"
] | permissive | AntoineChambert-Loir/mathlib | 64aabb896129885f12296a799818061bc90da1ff | 07be904260ab6e36a5769680b6012f03a4727134 | refs/heads/master | 1,693,187,631,771 | 1,636,719,886,000 | 1,636,719,886,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 17,412 | lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Simon Hudon, Mario Carneiro
-/
import algebra.group.defs
import logic.function.basic
/-!
# Basic lemmas about semigroups, monoids, and groups
This f... |
9fa8c3ce69d4761fa8c2c1756a908cf45beef9dd | 35677d2df3f081738fa6b08138e03ee36bc33cad | /src/order/filter/basic.lean | 46df0c3b8b2669fb63e82ac42c0205cdaef249ab | [
"Apache-2.0"
] | permissive | gebner/mathlib | eab0150cc4f79ec45d2016a8c21750244a2e7ff0 | cc6a6edc397c55118df62831e23bfbd6e6c6b4ab | refs/heads/master | 1,625,574,853,976 | 1,586,712,827,000 | 1,586,712,827,000 | 99,101,412 | 1 | 0 | Apache-2.0 | 1,586,716,389,000 | 1,501,667,958,000 | Lean | UTF-8 | Lean | false | false | 105,325 | lean | /-
Copyright (c) 2017 Johannes HΓΆlzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes HΓΆlzl, Jeremy Avigad
-/
import order.galois_connection order.zorn order.copy
import data.set.finite
/-! # Theory of filters on sets
## Main definitions
* `filter` : filter ... |
5c1f41c20ab913726e584693876c111f78c3f910 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/category_theory/category/Groupoid.lean | 95b5910e4ae5dad07872a4782b08f6564cfbc487 | [
"Apache-2.0"
] | permissive | jjgarzella/mathlib | 96a345378c4e0bf26cf604aed84f90329e4896a2 | 395d8716c3ad03747059d482090e2bb97db612c8 | refs/heads/master | 1,686,480,124,379 | 1,625,163,323,000 | 1,625,163,323,000 | 281,190,421 | 2 | 0 | Apache-2.0 | 1,595,268,170,000 | 1,595,268,169,000 | null | UTF-8 | Lean | false | false | 1,890 | lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import category_theory.single_obj
/-!
# Category of groupoids
This file contains the definition of the category `Groupoid` of all groupoids.
In this category obje... |
91b6ae9c31652881bfacc31be7eae7573df052e6 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/abstract_expr2.lean | 2e635b584d0e5709c8f07aefe7a99ef96825ac49 | [
"Apache-2.0"
] | permissive | soonhokong/lean | cb8aa01055ffe2af0fb99a16b4cda8463b882cd1 | 38607e3eb57f57f77c0ac114ad169e9e4262e24f | refs/heads/master | 1,611,187,284,081 | 1,450,766,737,000 | 1,476,122,547,000 | 11,513,992 | 2 | 0 | null | 1,401,763,102,000 | 1,374,182,235,000 | C++ | UTF-8 | Lean | false | false | 819 | lean | universes l1 l2 l3
constants (f : Ξ (X Y U : Type) (x1 x2 : X) (y1 y2 : Y) (Hx : x1 = x2) (Hy : y1 = y2), U)
constants (X : Type.{l1}) (Y : Type.{l2}) (U : Type.{l3})
constants (x1 x2 : X) (y1 y2 : Y) (Hx1 Hx2 : x1 = x2) (Hy1 Hy2 : y1 = y2)
#abstract_expr 0 f X Y U
#abstract_expr 0 f X Y U x1
#abstract_expr 0 f X Y U ... |
78aed0f2e1e0ac7578df5c0cdade7493c3781d26 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/analysis/convex/function.lean | 06b3abb2b315d282a6b2cb6b9e8cf34cb4803991 | [
"Apache-2.0"
] | permissive | urkud/mathlib | eab80095e1b9f1513bfb7f25b4fa82fa4fd02989 | 6379d39e6b5b279df9715f8011369a301b634e41 | refs/heads/master | 1,658,425,342,662 | 1,658,078,703,000 | 1,658,078,703,000 | 186,910,338 | 0 | 0 | Apache-2.0 | 1,568,512,083,000 | 1,557,958,709,000 | Lean | UTF-8 | Lean | false | false | 41,575 | lean | /-
Copyright (c) 2019 Alexander Bentkamp. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp, François Dupuis
-/
import analysis.convex.basic
import tactic.field_simp
import tactic.linarith
import tactic.ring
/-!
# Convex and concave functions
This fil... |
b4b10c3a10b3ace4e20767003379e63fae75a337 | 6e41ee3ac9b96e8980a16295cc21f131e731884f | /tests/lean/run/fibrant_class2.lean | cb5cef8959ed51302cf1584dc67bd2633d005dc6 | [
"Apache-2.0"
] | permissive | EgbertRijke/lean | 3426cfa0e5b3d35d12fc3fd7318b35574cb67dc3 | 4f2e0c6d7fc9274d953cfa1c37ab2f3e799ab183 | refs/heads/master | 1,610,834,871,476 | 1,422,159,801,000 | 1,422,159,801,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,156 | lean | inductive fibrant [class] (T : Type) : Type :=
fibrant_mk : fibrant T
axiom pi_fibrant {A : Type} {B : A β Type} [C1 : fibrant A] [C2 : Ξ x : A, fibrant (B x)] :
fibrant (Ξ x : A, B x)
attribute pi_fibrant [instance]
inductive path {A : Type} [fA : fibrant A] (a : A) : A β Type :=
idpath : path a a
axiom path_fibran... |
53131befbcd4b56101be528973b56d299b222fce | 63abd62053d479eae5abf4951554e1064a4c45b4 | /src/group_theory/quotient_group.lean | 751de973c2c37996424eb5593913ed665e26ce69 | [
"Apache-2.0"
] | permissive | Lix0120/mathlib | 0020745240315ed0e517cbf32e738d8f9811dd80 | e14c37827456fc6707f31b4d1d16f1f3a3205e91 | refs/heads/master | 1,673,102,855,024 | 1,604,151,044,000 | 1,604,151,044,000 | 308,930,245 | 0 | 0 | Apache-2.0 | 1,604,164,710,000 | 1,604,163,547,000 | null | UTF-8 | Lean | false | false | 7,520 | lean | /-
Copyright (c) 2018 Kevin Buzzard and Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Patrick Massot.
This file is to a certain extent based on `quotient_module.lean` by Johannes HΓΆlzl.
-/
import group_theory.coset
universes u v
names... |
4aa12d5655e704f60f2120fa61da6b6c75bfd4a6 | ff5230333a701471f46c57e8c115a073ebaaa448 | /library/init/category/default.lean | 3c871808431707404e105ac90f13de7f49378984 | [
"Apache-2.0"
] | permissive | stanford-cs242/lean | f81721d2b5d00bc175f2e58c57b710d465e6c858 | 7bd861261f4a37326dcf8d7a17f1f1f330e4548c | refs/heads/master | 1,600,957,431,849 | 1,576,465,093,000 | 1,576,465,093,000 | 225,779,423 | 0 | 3 | Apache-2.0 | 1,575,433,936,000 | 1,575,433,935,000 | null | UTF-8 | Lean | false | false | 434 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.category.applicative init.category.functor init.category.alternative
import init.category.monad init.category.lift init.category.lawful
... |
d6eab636b1ca1e42087d41904163b35b40fe7178 | dc253be9829b840f15d96d986e0c13520b085033 | /homotopy/fwedge.hlean | 63e8a90dd97a276e31757cac23d68c79ec44da6d | [
"Apache-2.0"
] | permissive | cmu-phil/Spectral | 4ce68e5c1ef2a812ffda5260e9f09f41b85ae0ea | 3b078f5f1de251637decf04bd3fc8aa01930a6b3 | refs/heads/master | 1,685,119,195,535 | 1,684,169,772,000 | 1,684,169,772,000 | 46,450,197 | 42 | 13 | null | 1,505,516,767,000 | 1,447,883,921,000 | Lean | UTF-8 | Lean | false | false | 15,246 | hlean | /-
Copyright (c) 2016 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Favonia
The Wedge Sum of a family of Pointed Types
-/
import homotopy.wedge ..move_to_lib ..choice ..pointed_pi
open eq is_equiv pushout pointed unit trunc_index ... |
2fb373f2500742b3dfd329d5b9ed3a078a3b62aa | 8d65764a9e5f0923a67fc435eb1a5a1d02fd80e3 | /src/ring_theory/subring.lean | 23a6b0046dad6affe9955c95dfbc2808c47b52ed | [
"Apache-2.0"
] | permissive | troyjlee/mathlib | e18d4b8026e32062ab9e89bc3b003a5d1cfec3f5 | 45e7eb8447555247246e3fe91c87066506c14875 | refs/heads/master | 1,689,248,035,046 | 1,629,470,528,000 | 1,629,470,528,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 36,186 | lean | /-
Copyright (c) 2020 Ashvni Narayanan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ashvni Narayanan
-/
import group_theory.subgroup
import ring_theory.subsemiring
/-!
# Subrings
Let `R` be a ring. This file defines the "bundled" subring type `subring R`, a type
... |
4d0b0df71da48d4aecc04465472cdd2cdeae901d | a9e33f9c83301c461f3c3ebc6799d9de1f6d4d20 | /notes/2019.10.14.prop_logic/prop_logic_test.lean | 3da1889c4b3a68de7e7ef9d1ebbf81562e6eb10d | [] | no_license | yl4df/Discrete-Mathematics | f1c9a6cf8cfb4686fb617637f69a481e1522f0c2 | c93ce9f6a6e36d194e350d9fa0a0360191e97fa0 | refs/heads/master | 1,598,714,938,443 | 1,572,275,647,000 | 1,572,275,647,000 | 218,074,726 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 13,735 | lean | import .prop_logic
/-
A logic is a "formal language" with
a mathematically defined syntax and a
mathematically defined semantics. The
syntax of a language defines the set
of legal expressions in the language
(sometimes called formula, well-formed
formula, sentences, etc). The semantics
then explains how to give a mean... |
c9549c6eb367f1adeadb593824851922802c16b0 | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/algebra/big_operators/basic.lean | 19a7a2e1b66be78732fe42a637925ba648765751 | [
"Apache-2.0"
] | permissive | agjftucker/mathlib | d634cd0d5256b6325e3c55bb7fb2403548371707 | 87fe50de17b00af533f72a102d0adefe4a2285e8 | refs/heads/master | 1,625,378,131,941 | 1,599,166,526,000 | 1,599,166,526,000 | 160,748,509 | 0 | 0 | Apache-2.0 | 1,544,141,789,000 | 1,544,141,789,000 | null | UTF-8 | Lean | false | false | 44,728 | lean | /-
Copyright (c) 2017 Johannes HΓΆlzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes HΓΆlzl
-/
import data.finset.fold
import data.equiv.mul_add
import tactic.abel
/-!
# Big operators
In this file we define products and sums indexed by finite sets (specifica... |
042db4a48d364228901081e3148dc4f10e352e7d | 92b13ae5cb04d78dd215ae736d93f5353e0e8e87 | /list_ext.lean | 73c84871994e9e1455a8703d495cba30251a2656 | [] | no_license | jroesch/exp-compiler | f2dec4f17e769e7f3b41429c41ece1f004a3f209 | 6efd4512c80df947361bdada12415bc166db5e7f | refs/heads/master | 1,585,267,520,150 | 1,469,047,597,000 | 1,469,047,597,000 | 63,471,055 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 757 | lean | import data.list
open prod
open list
definition cons_front {A} (f : A) : (list A Γ list A) β (list A Γ list A)
| cons_front (xs, ys) := (f :: xs, ys)
definition split_while {A : Type} (pred : A -> bool) : list A -> (list A Γ list A)
| split_while [] := ([], [])
| split_while (x :: xs) :=
if pred x = bool.tt th... |
869f1c6e3c6fc2d97f25a7f3a4713389ab743969 | e429a7c31201d4c56a2716f77a99c4831967b0de | /nat_extra.lean | 60b568b05da22a37be2bff92df1f54f4ade76b88 | [] | no_license | jthickstun/lean | cdb5ee8ec78294167d771a6167c0947419afa9eb | 8254b987f06be1f98ef2e0cc33b7d4655d77dc85 | refs/heads/master | 1,620,156,057,836 | 1,557,865,724,000 | 1,557,865,724,000 | 106,618,304 | 8 | 1 | null | null | null | null | UTF-8 | Lean | false | false | 2,765 | lean | import .logic_extra
import .definitions
namespace nat
lemma eq_eq {m n : β} (h : eq m n = tt) : m = n :=
begin
by_cases m = n with h1,
{ assumption },
{ simp [eq, h1] at h, contradiction }
end
lemma eq_of_eq {m n : β} (h : m = n) : eq m n = tt :=
by simp [eq,h]
/-
Useful stuff that should possibly be in the s... |
16204a1046dbfb8e68f27cd0c97a5e6f5365e12f | fffbc47930dc6615e66ece42324ce57a21d5b64b | /src/analysis/complex/exponential.lean | 2b80396ce09a3cca818ed03fb5366b1b3425f650 | [
"Apache-2.0"
] | permissive | skbaek/mathlib | 3caae8ae413c66862293a95fd2fbada3647b1228 | f25340175631cdc85ad768a262433f968d0d6450 | refs/heads/master | 1,588,130,123,636 | 1,558,287,609,000 | 1,558,287,609,000 | 160,935,713 | 0 | 0 | Apache-2.0 | 1,544,271,146,000 | 1,544,271,146,000 | null | UTF-8 | Lean | false | false | 60,450 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Abhimanyu Pallavi Sudhir, Jean Lo, Calle SΓΆnne
-/
import topology.instances.complex tactic.linarith data.complex.exponential
group_theory.quotient_group topology.metr... |
caa32411515c10996f7ac1c42f5d2de3e1f323cb | 31f556cdeb9239ffc2fad8f905e33987ff4feab9 | /tests/lean/run/ac_rfl.lean | 6e57a5e9cd69bd9463ef3a3bac0c85d50b78de20 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | tobiasgrosser/lean4 | ce0fd9cca0feba1100656679bf41f0bffdbabb71 | ebdbdc10436a4d9d6b66acf78aae7a23f5bd073f | refs/heads/master | 1,673,103,412,948 | 1,664,930,501,000 | 1,664,930,501,000 | 186,870,185 | 0 | 0 | Apache-2.0 | 1,665,129,237,000 | 1,557,939,901,000 | Lean | UTF-8 | Lean | false | false | 4,055 | lean | open Lean
instance : IsAssociative (Ξ± := Nat) HAdd.hAdd := β¨Nat.add_assocβ©
instance : IsCommutative (Ξ± := Nat) HAdd.hAdd := β¨Nat.add_commβ©
instance : IsNeutral HAdd.hAdd 0 := β¨Nat.zero_add, Nat.add_zeroβ©
instance : IsAssociative (Ξ± := Nat) HMul.hMul := β¨Nat.mul_assocβ©
instance : IsCommutative (Ξ± := Nat) HMul.hMul := ... |
801eacb168f4dcde4fa33e87ec29cbf4261ad719 | 9028d228ac200bbefe3a711342514dd4e4458bff | /src/data/polynomial/coeff.lean | ee0f703cdbafe82adf7f6572819b753b765a5278 | [
"Apache-2.0"
] | permissive | mcncm/mathlib | 8d25099344d9d2bee62822cb9ed43aa3e09fa05e | fde3d78cadeec5ef827b16ae55664ef115e66f57 | refs/heads/master | 1,672,743,316,277 | 1,602,618,514,000 | 1,602,618,514,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 6,394 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Johannes HΓΆlzl, Scott Morrison, Jens Wagemaker
-/
import data.polynomial.monomial
import data.finset.nat_antidiagonal
/-!
# Theory of univariate polynomials
The theorems ... |
462108fcc5e087bed0450ea9f6458138d21d14a2 | f4b5f8637e34e7de32a879ad3240aa214685b5a1 | /listr.lean | cda83b6bb006730f54ac5a035e4137570ce1cf8b | [] | no_license | leanparikshit/leanme | a5448628526d30a591d5349871692c14527ca195 | a869ee7d8131a0bba43509022f6da7cfe9424434 | refs/heads/master | 1,611,049,299,759 | 1,400,834,734,000 | 1,400,834,734,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,983 | lean | ----------------------------------------------------------------------------------------------------
--
-- list.lean
--
-- Experimenting with lists.
--
-- authors: Jeremy Avigad, Parikshit Khanna
--
----------------------------------------------------------------------------------------------------
import macros
impor... |
ce0bcb3013439c60f310c59a7e3b5216d82e6cdc | 0e175f34f8dca5ea099671777e8d7446d7d74227 | /library/init/meta/tactic.lean | fc9036e0ca09db73e25c081ea713c608d1ca163f | [
"Apache-2.0"
] | permissive | utensil-contrib/lean | b31266738071c654d96dac8b35d9ccffc8172fda | a28b9c8f78d982a4e82b1e4f7ce7988d87183ae8 | refs/heads/master | 1,670,045,564,075 | 1,597,397,599,000 | 1,597,397,599,000 | 287,528,503 | 0 | 0 | Apache-2.0 | 1,597,408,338,000 | 1,597,408,337,000 | null | UTF-8 | Lean | false | false | 74,583 | lean | /-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.function init.data.option.basic init.util
import init.control.combinators init.control.monad init.control.alternative init.control.monad... |
914e2809b256e24cecfadf20b2c36b5c9c028d50 | 6fca17f8d5025f89be1b2d9d15c9e0c4b4900cbf | /src/game/world10/level10.lean | c7cdedf357716809f6027b874e65f86e0c02d473 | [
"Apache-2.0"
] | permissive | arolihas/natural_number_game | 4f0c93feefec93b8824b2b96adff8b702b8b43ce | 8e4f7b4b42888a3b77429f90cce16292bd288138 | refs/heads/master | 1,621,872,426,808 | 1,586,270,467,000 | 1,586,270,467,000 | 253,648,466 | 0 | 0 | null | 1,586,219,694,000 | 1,586,219,694,000 | null | UTF-8 | Lean | false | false | 311 | lean | import game.world10.level9 -- hide
namespace mynat -- hide
/-
# Inequality world.
## Level 10: `le_succ_self`
Can you find the two-line proof?
-/
/- Lemma
For all naturals $a$, $a\le\operatorname{succ}(a).$
-/
lemma le_succ_self (a : mynat) : a β€ succ a :=
begin [nat_num_game]
end
end mynat -- hide
|
0c5d0e22d4c9468450a9d33a4692ab69f027da6f | 4727251e0cd73359b15b664c3170e5d754078599 | /src/linear_algebra/smodeq.lean | 7e74a8766c50452510dedd7c47511a38fac6da73 | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 2,939 | lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import data.polynomial.eval
import ring_theory.ideal.quotient
/-!
# modular equivalence for submodule
-/
open submodule
open_locale polynomial
variables {R : Type*} [ring R... |
99b81339f3069e5a57b1951ff0d94d448591dff0 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/nestedIssueMatch.lean | 8e945d809830ac191f1bfb48b14964690e8ba520 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 412 | lean | def g (t : Nat) : Nat := match t with
| (n+1) => match g n with
| 0 => 0
| m + 1 => match g (n - m) with
| 0 => 0
| m + 1 => g n
| 0 => 0
termination_by' sorry
decreasing_by sorry
attribute [simp] g
#check g._eq_1
#check g._eq_2
theorem ex3 : g (n + 1) = match g n with
| 0 => 0
| m + ... |
216303438b12e86e6bf0158d05fc231f58fcf386 | 5fbbd711f9bfc21ee168f46a4be146603ece8835 | /lean/natural_number_game/inequality/06.lean | 64a76d8bc31125b501d955dc0613db6e148cea9d | [
"LicenseRef-scancode-warranty-disclaimer"
] | no_license | goedel-gang/maths | 22596f71e3fde9c088e59931f128a3b5efb73a2c | a20a6f6a8ce800427afd595c598a5ad43da1408d | refs/heads/master | 1,623,055,941,960 | 1,621,599,441,000 | 1,621,599,441,000 | 169,335,840 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 303 | lean | theorem le_antisymm (a b : mynat) (hab : a β€ b) (hba : b β€ a) : a = b :=
begin
cases hab with n hn,
cases hba with m hm,
rw [hn, add_assoc] at hm,
symmetry at hm,
have hmnz := eq_zero_of_add_right_eq_self a (n + m) hm,
have hnz := add_right_eq_zero n m hmnz,
rw [hn, hnz],
ring,
end
|
d4dbdf5b76c4acd0087adb7aa8a2268f1ad19af6 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/list/sigma.lean | b24f8564ce41a06ae97b4c81c3dfee715e153d4f | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 25,866 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Sean Leather
-/
import data.list.range
import data.list.perm
/-!
# Utilities for lists of sigmas
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file... |
038a73ba802331dd739a39ac76419e6033cf7246 | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/data/rat/denumerable.lean | 9bff93be3f5a94e65ec9172247ca9426516e1ecc | [
"Apache-2.0"
] | permissive | stjordanis/mathlib | 51e286d19140e3788ef2c470bc7b953e4991f0c9 | 2568d41bca08f5d6bf39d915434c8447e21f42ee | refs/heads/master | 1,631,748,053,501 | 1,627,938,886,000 | 1,627,938,886,000 | 228,728,358 | 0 | 0 | Apache-2.0 | 1,576,630,588,000 | 1,576,630,587,000 | null | UTF-8 | Lean | false | false | 1,242 | lean | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import data.rat
import set_theory.cardinal
/-!
# Denumerability of β
This file proves that β is infinite, denumerable, and deduces that it has cardinality `omega`.
-/
... |
8d2bd4d0e1b7d1ebee7d86cc557064f177c246d4 | 7282d49021d38dacd06c4ce45a48d09627687fe0 | /examples/lean/set.lean | 0afd2e6f384e8de5b741c29e5cde4cb0557a8236 | [
"Apache-2.0"
] | permissive | steveluc/lean | 5a0b4431acefaf77f15b25bbb49294c2449923ad | 92ba4e8b2d040a799eda7deb8d2a7cdd3e69c496 | refs/heads/master | 1,611,332,256,930 | 1,391,013,244,000 | 1,391,013,244,000 | 16,361,079 | 1 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 926 | lean | import macros
definition Set (A : Type) : Type := A β Bool
definition element {A : Type} (x : A) (s : Set A) := s x
infix 60 β : element
definition subset {A : Type} (s1 : Set A) (s2 : Set A) := β x, x β s1 β x β s2
infix 50 β : subset
theorem subset_trans {A : Type} {s1 s2 s3 : Set A} (H1 : s1 β s2) (H2 : s2 β s3)... |
df32479a0d409f4504b8377753bdd7606482c7d3 | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/topology/algebra/infinite_sum.lean | 7b97b5ab67c2a284c1e0912d75fe6208d8284f9c | [
"Apache-2.0"
] | permissive | stjordanis/mathlib | 51e286d19140e3788ef2c470bc7b953e4991f0c9 | 2568d41bca08f5d6bf39d915434c8447e21f42ee | refs/heads/master | 1,631,748,053,501 | 1,627,938,886,000 | 1,627,938,886,000 | 228,728,358 | 0 | 0 | Apache-2.0 | 1,576,630,588,000 | 1,576,630,587,000 | null | UTF-8 | Lean | false | false | 51,268 | lean | /-
Copyright (c) 2017 Johannes HΓΆlzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes HΓΆlzl
-/
import algebra.big_operators.intervals
import topology.instances.real
import topology.algebra.module
import algebra.indicator_function
import data.equiv.encodable.lat... |
a885e643de6cb27ee9697c188f4e635509de1e04 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/category_theory/monad/algebra.lean | ee86aef2e4767e9a5267e8b42f1d0f553ba3cd07 | [
"Apache-2.0"
] | permissive | robertylewis/mathlib | 3d16e3e6daf5ddde182473e03a1b601d2810952c | 1d13f5b932f5e40a8308e3840f96fc882fae01f0 | refs/heads/master | 1,651,379,945,369 | 1,644,276,960,000 | 1,644,276,960,000 | 98,875,504 | 0 | 0 | Apache-2.0 | 1,644,253,514,000 | 1,501,495,700,000 | Lean | UTF-8 | Lean | false | false | 12,105 | lean | /-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison, Bhavik Mehta
-/
import category_theory.monad.basic
import category_theory.adjunction.basic
import category_theory.reflects_isomorphisms
/-!
# Eilenberg-Moore (co)algeb... |
69892601f9066de622eeec59b1c46efe050a8187 | 853df553b1d6ca524e3f0a79aedd32dde5d27ec3 | /src/order/complete_lattice.lean | 33d6a628a7dbdc48577fb3c136fa5abc7c8fc2bf | [
"Apache-2.0"
] | permissive | DanielFabian/mathlib | efc3a50b5dde303c59eeb6353ef4c35a345d7112 | f520d07eba0c852e96fe26da71d85bf6d40fcc2a | refs/heads/master | 1,668,739,922,971 | 1,595,201,756,000 | 1,595,201,756,000 | 279,469,476 | 0 | 0 | null | 1,594,696,604,000 | 1,594,696,604,000 | null | UTF-8 | Lean | false | false | 40,759 | lean | /-
Copyright (c) 2017 Johannes HΓΆlzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes HΓΆlzl
-/
import order.bounds
/-!
# Theory of complete lattices
## Main definitions
* `Sup` and `Inf` are the supremum and the infimum of a set;
* `supr (f : ΞΉ β Ξ±)` and `in... |
eede5f817fe69c8383f1b6b766779979d492fda5 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/data/holor.lean | 35699760c4404f13a86f35093aa4e9cac9e21973 | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 14,762 | lean | /-
Copyright (c) 2018 Alexander Bentkamp. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp
-/
import algebra.module.pi
import algebra.big_operators.basic
/-!
# Basic properties of holors
Holors are indexed collections of tensor coefficients. Confusin... |
56b4047f2f34aee3932586fc16e60fc8ac80f5f5 | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/tactic/ext.lean | bdc8393ce92df010db3603cfed7ddee008b449b2 | [
"Apache-2.0"
] | permissive | dupuisf/mathlib | 62de4ec6544bf3b79086afd27b6529acfaf2c1bb | 8582b06b0a5d06c33ee07d0bdf7c646cae22cf36 | refs/heads/master | 1,669,494,854,016 | 1,595,692,409,000 | 1,595,692,409,000 | 272,046,630 | 0 | 0 | Apache-2.0 | 1,592,066,143,000 | 1,592,066,142,000 | null | UTF-8 | Lean | false | false | 14,685 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
import tactic.rcases
import data.sum
import logic.function.basic
universes uβ uβ
open interactive interactive.types
open lean.parser nat tactic
/--
`derive_struct_ext_le... |
12da63e8127dcdd61d6c1fd829abd05655614fde | 4fa161becb8ce7378a709f5992a594764699e268 | /src/algebra/group_with_zero.lean | d85029d8f66297ac2f6949371364193f8c50fe11 | [
"Apache-2.0"
] | permissive | laughinggas/mathlib | e4aa4565ae34e46e834434284cb26bd9d67bc373 | 86dcd5cda7a5017c8b3c8876c89a510a19d49aad | refs/heads/master | 1,669,496,232,688 | 1,592,831,995,000 | 1,592,831,995,000 | 274,155,979 | 0 | 0 | Apache-2.0 | 1,592,835,190,000 | 1,592,835,189,000 | null | UTF-8 | Lean | false | false | 22,803 | lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import algebra.group.commute
import algebra.ring
import tactic.push_neg
/-!
# Groups with an adjoined zero element
This file describes structures that are not usual... |
588ee3cbde5cbf82cc27b506ccb0cea28bf71c4e | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/category_theory/limits/constructions/limits_of_products_and_equalizers.lean | e78de497fcaa48f1ccc8def48a9d6cad9c9bab72 | [
"Apache-2.0"
] | permissive | robertylewis/mathlib | 3d16e3e6daf5ddde182473e03a1b601d2810952c | 1d13f5b932f5e40a8308e3840f96fc882fae01f0 | refs/heads/master | 1,651,379,945,369 | 1,644,276,960,000 | 1,644,276,960,000 | 98,875,504 | 0 | 0 | Apache-2.0 | 1,644,253,514,000 | 1,501,495,700,000 | Lean | UTF-8 | Lean | false | false | 13,186 | lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Scott Morrison
-/
import category_theory.limits.shapes.equalizers
import category_theory.limits.shapes.finite_products
import category_theory.limits.preserves.shapes.produc... |
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